$ \begin{aligned} 解:原式&=\sqrt {x^{2} +\frac {1}{x^{2} }+2} -\sqrt {x^{2} +\frac {1}{x^{2} }-2} \\ &=\sqrt {(x+\frac {1}{x})^{2} } -\sqrt {(x-\frac {1}{x})^{2} } \\ &=|x+\frac {1}{x}|-|x-\frac {1}{x}| \\ &=x+\frac {1}{x}+x-\frac {1}{x}& \\ &=2x \\ \end{aligned}$